Completeness and Performance
A motion planner is said to be complete if the planner in finite time either produces a solution or correctly reports that there is none. Most complete algorithms are geometry-based. The performance of a complete planner is assessed by its computational complexity.
Resolution completeness is the property that the planner is guaranteed to find a path if the resolution of an underlying grid is fine enough. Most resolution complete planners are grid-based. The computational complexity of resolution complete planners is dependent on the number of points in the underlying grid, which is O(1/hd), where h is the resolution (the length of one side of a grid cell) and d is the configuration space dimension.
Probabilistic completeness is the property that as more “work” is performed, the probability that the planner fails to find a path, if one exists, asymptotically approaches zero. Several sample-based methods are probabilistically complete. The performance of a probabilistically complete planner is measured by the rate of convergence.
Incomplete planners do not always produce a feasible path when one exists. Sometimes incomplete planners do work well in practice.
Read more about this topic: Motion Planning
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